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When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t), where t represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity I, of the incident beam. dI = kI. dt Find the constant of proportionality k, where k = What is the intensity of the beam 12 feet below the surface? (Give your answer in terms of In. Round any constants or coefficients to five decimal places.)

When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t), where t represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity I, of the incident beam. dI = kI. dt Find the constant of proportionality k, where k = What is the intensity of the beam 12 feet below the surface? (Give your answer in terms of In. Round any constants or coefficients to five decimal places.)

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t), wheret represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity I, of the incident beam. dI Find the constant of proportionality k, where dt kI. k = What is the intensity of the beam 12 feet below the surface? (Give your answer in terms of In. Round any constants or coefficients to five decimal places.)
Transcribed Image Text:When a vertical beam of light passes through a transparent medium, the rate at which its intensity I decreases is proportional to I(t), wheret represents the thickness of the medium (in feet). In clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity I, of the incident beam. dI Find the constant of proportionality k, where dt kI. k = What is the intensity of the beam 12 feet below the surface? (Give your answer in terms of In. Round any constants or coefficients to five decimal places.)
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